# 5G Polar Codes Dr. Erdal Arikan

Dr. Erdal Arikan (1958 -) of Bilkent University, Turkey, recieved his PhD in MIT at the age of 27.

Huawei Award: The Father of Polar Codes (极化码)

Industry watchers believe that the selection of polar coding as the channel coding technique for control channels for 5G communications system may have put Huawei at the forefront in the 5G race (27 Gbps in 2016).

1 Gbps = 1000 Mbps

5G Basic Explained:

Part 1: The Math behind 5G Polar Codes

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Part 2:

Part 3:

Notations:

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$\displaystyle F = \begin {bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}$

$A = \begin{pmatrix} a_{11} & a_{12}& \ldots & a_{1n}\\ a_{21} & a_{22} & \ldots & a_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ a_{n1}& a_{n2} &\ldots & a_{nn} \end{pmatrix}$$B = \begin{pmatrix} b_{11} & b_{12}& \ldots & b_{1n}\\ b_{21} & b_{22} & \ldots & b_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ b_{n1}& b_{n2} &\ldots & b_{nn} \end{pmatrix}$$\displaystyle F^{{\otimes}{n}} = F^{{\otimes}{(n-1) }} \otimes F = \begin {bmatrix} F^{{\otimes}{(n-1) }} & 0\\ F^{{\otimes}{(n-1) }} & F^{{\otimes}{(n-1) }} \end{bmatrix}$$A \otimes B = \begin {pmatrix} a_{11}B & a_{12}B & \ldots & a_{1n}B\\ a_{21}B& a_{22}B & \ldots & a_{2n}B\\ \vdots & \vdots & \ddots & \vdots\\ a_{n1}B & a_{n2}B &\ldots & a_{nn}B \end{pmatrix}$